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We present four ab initio axisymmetric core-collapse supernova simulationsfor 12, 15, 20, and 25 $M_\odot$ progenitors. All of the simulations yieldexplosions and have been evolved for at least 1.2 seconds after core bounce and1 second after material first becomes unbound. Simulations were computed withour Chimera code employing spectral neutrino transport, special and generalrelativistic transport effects, and state-of-the-art neutrino interactions.Continuing the evolution beyond 1 second allows explosions to develop morefully and the processes powering the explosions to become more clearly evident.We compute explosion energy estimates, including the binding energy of thestellar envelope outside the shock, of 0.34, 0.88, 0.38, and 0.70 B ($10^{51}$ergs) and increasing at 0.03, 0.15, 0.19, and 0.52 B s$^{-1}$, respectively,for the 12, 15, 20, and 25 $M_\odot$ models. Three models developed pronouncedprolate shock morphologies, while the 20 $M_\odot$ model, though exhibitinglobes and accretion streams like the other models, develops an approximatelyspherical, off-center shock as the explosion begins and then becomes moderatelyprolate $\sim$600 ms after bounce. This reduces the explosion energy relativeto the other models by reducing mass accretion during the critical explosionpower-up phase. We examine the growth of the explosion energy in our modelsthrough detailed analyses of the energy sources and flows. We find that the 12and 20 $M_\odot$ models have explosion energies comparable to that of the lowerrange of observed explosion energies while the 15 and 25 $M_\odot$ models arewithin the range of observed explosion energies, particularly considering therate at which their explosion energies are increasing. The ejected $^{56}$Nimasses given by our models are all within observational limits as are theproto-neutron star masses and kick velocities. (Truncated)

The Development of Explosions in Axisymmetric Ab Initio Core-Collapse Supernova Simulations of 12-25 $M_\odot$ Stars